library(rstan)
Loading required package: StanHeaders
Loading required package: ggplot2
rstan (Version 2.21.1, GitRev: 2e1f913d3ca3)
For execution on a local, multicore CPU with excess RAM we recommend calling
options(mc.cores = parallel::detectCores()).
To avoid recompilation of unchanged Stan programs, we recommend calling
rstan_options(auto_write = TRUE)
library(survival)
library(tidyverse)
Registered S3 methods overwritten by 'dbplyr':
method from
print.tbl_lazy
print.tbl_sql
── Attaching packages ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── tidyverse 1.3.1 ──
✓ tibble 3.1.4 ✓ dplyr 1.0.7
✓ tidyr 1.1.3 ✓ stringr 1.4.0
✓ readr 2.0.1 ✓ forcats 0.5.1
✓ purrr 0.3.4
── Conflicts ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
x tidyr::extract() masks rstan::extract()
x dplyr::filter() masks stats::filter()
x dplyr::lag() masks stats::lag()
library(tidybayes)
library(scales)
Attaching package: ‘scales’
The following object is masked from ‘package:purrr’:
discard
The following object is masked from ‘package:readr’:
col_factor
library(survminer)
Loading required package: ggpubr
Registered S3 method overwritten by 'data.table':
method from
print.data.table
# data, parameters, model and generated quantities blocks
Stan_exponential_survival_model <- "
data{
int <lower=1> N_uncensored;
int <lower=1> N_censored;
int <lower=0> numCovariates;
matrix[N_censored, numCovariates] X_censored;
matrix[N_uncensored, numCovariates] X_uncensored;
vector <lower=0>[N_censored] times_censored;
vector <lower=0>[N_uncensored] times_uncensored;
}
parameters{
vector[numCovariates] beta; //regression coefficients
real alpha; //intercept
}
model{
beta ~ normal(0,10); //prior on regression coefficients
alpha ~ normal(0,10); //prior on intercept
target += exponential_lpdf(times_uncensored | exp(alpha+X_uncensored * beta)); //log-likelihood part for uncensored times
target += exponential_lccdf(times_censored | exp(alpha+X_censored * beta)); //log-likelihood for censored times
}
generated quantities{
vector[N_uncensored] times_uncensored_sampled; //prediction of death
for(i in 1:N_uncensored) {
times_uncensored_sampled[i] = exponential_rng(exp(alpha+X_uncensored[i,]* beta));
}
}
"
# prepare the data
set.seed(42);
require (tidyverse);
data <- read_csv('../data/necessary_fields.csv')
Rows: 2066 Columns: 7
── Column specification ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (1): host_type
dbl (1): duration_months
lgl (5): major_releases, censored, high_rev_freq, multi_repo, high_author_count
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
N <- nrow (data);
data$high_rev_freq <- car::recode(data$high_rev_freq, "'TRUE' = 0; 'FALSE' = 1")
data$censored <- car::recode(data$censored, "'TRUE' = 0; 'FALSE' = 1")
X <- as.matrix(pull(data, high_rev_freq));
is_censored <- pull(data, censored)==0;
times <- pull(data, duration_months);
msk_censored <- is_censored == 1;
N_censored <- sum(msk_censored);
# put data into a list for Stan
Stan_data <- list (N_uncensored = N - N_censored,
N_censored = N_censored,
numCovariates = ncol(X),
X_censored = as.matrix(X[msk_censored,]),
X_uncensored = as.matrix(X[!msk_censored ,]),
times_censored = times[msk_censored],
times_uncensored = times[!msk_censored])
# fit Stan model
require(rstan)
exp_surv_model_fit <- suppressMessages(stan(model_code = Stan_exponential_survival_model, data = Stan_data))
sh: Data/bayesian: No such file or directory
sh: clang++ -mmacosx-version-min=10.13: command not found
Warning in system2(CXX, args = ARGS) : error in running command
Warning in file.remove(c(unprocessed, processed)) :
cannot remove file '/var/folders/q8/7tchbyvd1dj3hkgw5ffkk6ph0000gp/T//RtmpeCjqex/file9c0835d1db07.stan', reason 'No such file or directory'
SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 1).
Chain 1:
Chain 1: Gradient evaluation took 0.000522 seconds
Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 5.22 seconds.
Chain 1: Adjust your expectations accordingly!
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Chain 1:
SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 2).
Chain 2:
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Chain 2:
SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 3).
Chain 3:
Chain 3: Gradient evaluation took 0.000201 seconds
Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 2.01 seconds.
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SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 4).
Chain 4:
Chain 4: Gradient evaluation took 0.0002 seconds
Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 2 seconds.
Chain 4: Adjust your expectations accordingly!
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# print model fit
print(get_seed(exp_surv_model_fit))
[1] 1781592037
# print fit summary
fit_summary <- summary(exp_surv_model_fit)
print(fit_summary$summary)
mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
beta[1] -0.3649827 0.002232828 0.07775502 -0.5159804 -0.4190547 -0.3647768 -0.3122201 -0.2109212 1212.680 1.0015373
alpha -4.5545737 0.001898961 0.06552380 -4.6873049 -4.5989760 -4.5528496 -4.5100872 -4.4313723 1190.601 1.0033388
times_uncensored_sampled[1] 132.6874082 2.121700110 134.00227672 2.8319295 36.4495443 89.7169422 186.4951063 487.9319018 3988.929 0.9994060
times_uncensored_sampled[2] 133.5689338 2.071923203 131.26947611 3.5702591 39.9063472 95.1670550 181.4523861 487.5108726 4014.026 1.0002691
times_uncensored_sampled[3] 134.8286784 2.217946247 138.27126474 2.9770698 38.5223488 93.4905547 185.4026691 488.4504457 3886.528 0.9997243
times_uncensored_sampled[4] 136.0198469 2.212850972 137.63204679 2.7234239 38.1322622 90.8373023 187.6302059 498.9298274 3868.431 1.0000950
times_uncensored_sampled[5] 134.4376128 2.176116701 133.97287843 3.7846059 38.7642386 91.7887850 186.9413625 495.6214616 3790.264 1.0021473
times_uncensored_sampled[6] 135.4165352 2.198448004 132.44705770 3.1923859 39.8255634 96.8336629 187.6686040 490.7169799 3629.545 1.0005374
times_uncensored_sampled[7] 139.8119162 2.294297454 141.57790135 4.1169510 40.9278116 96.0606123 192.2967936 526.6133416 3807.952 0.9995263
times_uncensored_sampled[8] 137.6954022 2.040576194 134.78179704 3.5351123 39.2472526 97.5326819 191.4360844 493.7552786 4362.715 1.0000152
times_uncensored_sampled[9] 136.1238977 2.136521840 135.65093734 3.3500869 39.3982507 94.7162320 190.1865676 491.0063090 4031.168 1.0003850
times_uncensored_sampled[10] 94.7821688 1.539521854 95.87968998 2.4918721 26.6021636 65.3213917 130.7728017 356.2753139 3878.658 1.0000222
times_uncensored_sampled[11] 137.1595561 2.299564861 138.00910880 3.5643348 38.1216226 92.5895703 191.3460877 507.0725713 3601.838 0.9991946
times_uncensored_sampled[12] 135.1701665 2.084413547 132.26309832 3.4942368 39.3934383 93.5070097 191.1570572 477.8703389 4026.332 0.9996017
times_uncensored_sampled[13] 137.6016479 2.193185524 137.31510192 3.1744808 40.3921844 97.9480871 186.2470856 519.9309017 3919.998 1.0003844
times_uncensored_sampled[14] 138.3907711 2.170488768 138.12386992 3.7176894 39.4772865 95.6273592 190.4885172 499.6262344 4049.696 1.0000400
times_uncensored_sampled[15] 94.0215749 1.495059339 91.42272356 2.2724948 26.7715300 66.2028400 133.0524473 333.0054722 3739.310 0.9994917
times_uncensored_sampled[16] 136.7803735 2.228600608 138.45309173 3.3170996 39.8902211 92.7244536 191.6840199 513.9880298 3859.587 1.0002426
times_uncensored_sampled[17] 132.8014655 2.125140893 132.69908138 3.6749703 38.9717079 91.0404926 185.4382082 485.8952870 3899.064 0.9997887
times_uncensored_sampled[18] 135.4579499 2.174827360 135.51159184 3.7484822 40.1920075 94.8009090 185.6466213 493.0693466 3882.427 1.0000167
times_uncensored_sampled[19] 97.1965100 1.548170422 96.31068704 2.9926589 28.7559922 69.0085310 133.7994761 363.5654345 3870.004 1.0008745
times_uncensored_sampled[20] 91.6542876 1.405038293 88.77274272 1.8324030 26.5906447 64.3320156 128.3492961 325.2086720 3991.930 1.0001730
times_uncensored_sampled[21] 136.4361217 2.143989338 135.76242592 3.5784434 38.2992114 94.6134407 192.9765517 502.1270810 4009.719 1.0005456
times_uncensored_sampled[22] 137.2823231 2.253657521 135.52312535 4.1268955 41.3109175 95.4053943 191.7666291 504.2493900 3616.188 0.9993997
times_uncensored_sampled[23] 133.9494976 2.113569528 135.17099650 2.7333145 38.9769816 92.3348048 183.7625084 489.0476277 4090.100 0.9997809
times_uncensored_sampled[24] 140.0721131 2.231795706 139.91323468 3.8255814 40.4150603 98.1576089 194.3122398 519.2952336 3930.146 1.0001119
times_uncensored_sampled[25] 135.4089451 2.192686994 134.19440961 3.5525630 40.2017688 95.6346322 188.8038006 494.2907665 3745.550 0.9996147
times_uncensored_sampled[26] 98.0401415 1.520796463 98.90114880 2.2501314 27.0451514 65.0992112 136.9478797 355.7213883 4229.222 0.9995280
times_uncensored_sampled[27] 96.4010648 1.674855830 100.96631074 2.0794912 27.3760581 63.9970614 130.3797832 373.4257306 3634.110 0.9998301
times_uncensored_sampled[28] 135.7643439 2.114407928 134.23160519 3.2244823 41.1650505 96.8530747 185.6671581 478.5990351 4030.250 0.9995103
times_uncensored_sampled[29] 94.5356062 1.536552842 94.29507168 2.5784179 27.2351844 66.2691384 132.2976458 354.4975318 3766.023 1.0002958
times_uncensored_sampled[30] 95.8141589 1.602463360 97.88923630 2.4084404 27.6145962 65.9222659 130.9119950 351.7248928 3731.588 0.9994790
times_uncensored_sampled[31] 138.8237278 2.218599560 140.79109249 3.0371933 40.1767605 96.0277846 193.9579518 522.9393538 4027.101 0.9995683
times_uncensored_sampled[32] 137.4225660 2.333135235 140.94515239 3.9501599 38.9754700 93.3019589 187.6626566 515.0759954 3649.392 1.0001848
times_uncensored_sampled[33] 96.0305942 1.585831659 96.32104425 2.5296587 29.0271234 66.6241290 133.1045366 359.0082642 3689.166 1.0005223
times_uncensored_sampled[34] 96.5429896 1.552022708 97.68540795 2.3535224 26.6657391 67.5228065 133.0536843 363.5748228 3961.533 0.9999344
times_uncensored_sampled[35] 96.0888860 1.537683290 96.10228103 2.3081371 27.3769903 66.3915700 134.1033510 354.4852771 3906.012 0.9996702
times_uncensored_sampled[36] 139.9622282 2.205924753 139.82965732 3.3599433 38.8298554 96.2264720 195.6529209 521.0919368 4018.067 1.0007824
times_uncensored_sampled[37] 96.2366612 1.507375668 95.31584199 2.2723477 27.2264199 66.8482072 133.1978449 351.6069654 3998.409 0.9998617
times_uncensored_sampled[38] 137.1468847 2.178582277 137.83085076 3.8122744 40.9827772 94.5387018 188.0067508 512.4875811 4002.625 1.0007099
times_uncensored_sampled[39] 136.9559731 2.129868776 131.18256265 3.8809618 40.5699390 97.6518571 194.1222264 482.4515947 3793.556 1.0002314
times_uncensored_sampled[40] 134.3941722 2.198200490 134.58333773 2.9759864 38.6177341 92.5137427 184.8347685 506.6518075 3748.418 1.0002629
times_uncensored_sampled[41] 137.2649493 2.136017336 136.10210944 3.5752843 40.6257043 95.7336082 191.5560511 492.4909464 4059.945 0.9999956
times_uncensored_sampled[42] 139.3287098 2.206801880 139.38581867 3.2472102 41.7953361 97.3158537 193.9968848 524.4541341 3989.427 0.9994068
times_uncensored_sampled[43] 137.3903065 2.117193971 138.26868262 3.8106854 39.3034864 95.2655681 188.0904639 511.0993348 4265.072 0.9996977
times_uncensored_sampled[44] 137.8959316 2.141077542 137.33798690 2.8254635 39.1666214 94.8520110 194.8051759 503.2900503 4114.495 1.0003376
times_uncensored_sampled[45] 138.9513600 2.225880746 138.54733603 3.7872933 40.7285125 96.9378019 193.8078153 502.5378217 3874.294 0.9995231
times_uncensored_sampled[46] 136.7308339 2.178832898 138.29285366 3.5472102 39.7428320 94.6886941 187.3119298 486.7683975 4028.577 0.9994574
times_uncensored_sampled[47] 97.4584434 1.536392980 98.06888211 2.0659110 27.2722133 66.6048780 134.8860481 370.4744286 4074.345 0.9997953
times_uncensored_sampled[48] 137.5023873 2.258224851 136.13490360 3.2084824 38.0729219 97.0283203 191.4874359 512.7140825 3634.165 0.9996261
times_uncensored_sampled[49] 96.2697539 1.489124116 94.33937803 2.8083081 27.9572684 67.1286090 134.4584238 345.2488083 4013.509 0.9996927
times_uncensored_sampled[50] 133.6061072 2.165873290 133.73423312 2.9395476 39.4957625 94.0515647 183.5115194 488.1563007 3812.581 0.9997716
times_uncensored_sampled[51] 95.8438199 1.523088604 96.61732877 2.5382947 27.0727459 67.2519448 132.7650623 355.3816679 4024.016 1.0012169
times_uncensored_sampled[52] 140.9192254 2.257014946 142.93106388 3.6001100 41.7362838 96.4259113 194.9556417 516.8226323 4010.369 0.9999976
times_uncensored_sampled[53] 133.8834902 2.141579977 133.90763532 3.4298326 39.4317680 89.9654327 187.5873042 488.6131871 3909.688 1.0004141
times_uncensored_sampled[54] 138.3663070 2.301008963 140.87285108 3.9143894 40.0334752 95.1300446 188.8701944 516.5999622 3748.159 0.9994086
times_uncensored_sampled[55] 133.8124881 2.145927440 134.13012079 3.9903781 39.7243492 91.1799349 187.9093366 493.8997459 3906.812 1.0003107
times_uncensored_sampled[56] 134.1169729 2.134546055 132.40372691 2.7036041 39.6870738 94.5609824 188.2669877 479.6612769 3847.595 0.9994266
times_uncensored_sampled[57] 93.8980869 1.497776663 94.75411436 2.3746733 26.9215121 64.8648469 129.2218706 348.2839060 4002.230 1.0009670
times_uncensored_sampled[58] 138.1174078 2.162763220 136.51879611 3.6991589 39.4868168 95.2712766 192.5371805 497.1312827 3984.437 1.0015540
times_uncensored_sampled[59] 134.4651870 2.111079764 136.03763642 3.3822801 37.9554707 92.5136874 187.4853175 498.7337323 4152.493 0.9998781
times_uncensored_sampled[60] 139.8327213 2.342794157 140.93105520 3.6301434 39.5455319 94.7607735 192.0568379 517.4477698 3618.638 0.9997617
times_uncensored_sampled[61] 136.2742391 2.438046602 139.57288014 3.0803738 37.5263300 94.8177578 190.2470968 495.8188581 3277.314 1.0006995
times_uncensored_sampled[62] 135.1607383 2.128929359 135.26098408 2.7878667 37.7186939 94.6196479 191.1354146 479.4386337 4036.664 0.9995670
times_uncensored_sampled[63] 135.2470615 2.192055843 138.52094513 3.4684822 38.2161006 92.5615273 186.4949739 507.9012568 3993.261 0.9993113
times_uncensored_sampled[64] 135.3424605 2.243042549 135.84608939 2.9191510 39.3841249 92.7574288 186.5482119 494.3895008 3667.915 1.0006108
times_uncensored_sampled[65] 135.1405810 2.111391276 134.68114650 3.5005091 40.0071145 93.7491233 190.2608680 484.5130155 4068.892 0.9991186
times_uncensored_sampled[66] 91.7364705 1.490034607 91.13875367 2.4822086 26.7021565 64.4118084 125.9383157 342.4072528 3741.222 0.9995606
times_uncensored_sampled[67] 139.7910595 2.185952933 139.63083488 3.2654528 39.0764083 99.2906866 194.5613763 510.0090479 4080.196 0.9994884
times_uncensored_sampled[68] 135.0191620 2.256558809 136.09009890 2.9777031 37.6232936 91.1868727 188.5479612 510.5580013 3637.138 0.9999357
times_uncensored_sampled[69] 96.3066726 1.559727877 97.93169069 2.5503495 27.5505327 65.4624417 133.7871626 360.7555705 3942.292 1.0002989
times_uncensored_sampled[70] 139.3171320 2.160383032 137.67069963 3.3680352 39.8252196 95.2233174 197.2352111 518.9269960 4060.893 0.9992903
times_uncensored_sampled[71] 135.6574831 2.151444856 138.16713011 3.3830935 37.3416934 94.2791316 186.3510097 506.2150776 4124.288 0.9997161
times_uncensored_sampled[72] 93.9951957 1.499023790 93.72521941 2.5329162 26.5968717 65.5350747 130.7835448 335.1167144 3909.272 1.0005162
times_uncensored_sampled[73] 96.9970985 1.526729225 97.41149758 2.7163729 27.7512095 65.5314920 134.4233130 355.7020917 4070.956 1.0008935
times_uncensored_sampled[74] 140.3125457 2.331101938 142.94348395 3.8027291 38.4905007 96.0303908 194.2493044 531.5577872 3760.159 0.9995171
times_uncensored_sampled[75] 138.6640864 2.432262353 139.68724747 3.4157998 39.9455458 97.3505102 191.1761148 514.1924127 3298.319 1.0001069
times_uncensored_sampled[76] 137.1412113 2.206281990 137.69786615 3.9273375 41.4939549 94.8178913 188.5469096 521.3583534 3895.223 0.9995407
times_uncensored_sampled[77] 141.0658124 2.204367006 141.04744921 3.6378271 41.0848469 98.0411310 196.8092895 529.5515640 4094.140 0.9996702
times_uncensored_sampled[78] 137.1473772 2.103980734 134.50532092 3.1822686 40.0753288 97.2504269 189.8149312 502.4076220 4086.913 0.9999990
times_uncensored_sampled[79] 134.1241423 2.164493345 134.18322539 3.2759498 38.7837483 92.2257152 187.1611319 498.3950846 3843.120 1.0002356
times_uncensored_sampled[80] 136.3176563 2.294870199 139.54523135 4.5506186 38.6971292 91.4142683 186.9817591 526.2453750 3697.547 1.0002236
times_uncensored_sampled[81] 94.8908804 1.524912560 94.29482960 2.5801349 26.1272132 65.1896881 133.3584653 338.4507867 3823.718 0.9998350
times_uncensored_sampled[82] 95.7510508 1.542113974 95.70360799 2.2393064 27.1836222 66.9440756 133.0073902 355.2384425 3851.445 0.9997376
times_uncensored_sampled[83] 92.5524427 1.563423189 96.37416412 2.1329944 25.8566389 62.4966307 129.4590233 366.7484340 3799.865 1.0000561
times_uncensored_sampled[84] 95.5561583 1.508490258 95.74040677 2.3633874 27.4078948 66.9862879 134.5906970 355.8743675 4028.149 1.0004378
times_uncensored_sampled[85] 94.9599036 1.514618283 98.25724584 2.7180414 25.7951090 64.9186137 130.9362143 368.8392397 4208.456 0.9995143
times_uncensored_sampled[86] 139.5095668 2.333776912 141.46558773 3.5264812 40.0612705 95.2568817 192.0983541 519.3689488 3674.370 1.0001556
times_uncensored_sampled[87] 132.6709022 2.292633411 133.42729498 3.3576725 36.8865469 93.0989771 184.3824289 495.0357334 3387.038 0.9998777
times_uncensored_sampled[88] 94.2938280 1.435716829 95.37421979 2.2327655 27.3102945 63.9783467 128.1350643 347.5332280 4412.903 1.0013069
times_uncensored_sampled[89] 135.7667868 2.166569727 136.11472275 3.7644703 39.2543046 94.8479456 188.3003221 491.5146699 3946.979 0.9997486
times_uncensored_sampled[90] 93.7145469 1.498004575 92.99583822 2.4359146 26.8761892 65.3872135 130.9443147 334.2104668 3853.903 1.0000057
times_uncensored_sampled[91] 138.1580236 2.375932351 135.74635543 4.0676492 41.2572274 97.8246092 192.4081017 504.7281456 3264.286 1.0010398
times_uncensored_sampled[92] 94.5134600 1.537972584 97.17953050 2.1069141 26.3810416 63.3921128 132.6665275 353.4782425 3992.569 1.0008520
times_uncensored_sampled[93] 136.3432353 2.259713366 139.27222642 4.0845205 39.4949419 92.3869815 186.0876962 512.6528484 3798.589 0.9997829
times_uncensored_sampled[94] 96.0213041 1.442528587 94.15896587 2.3620150 27.5832052 66.3557851 137.0656443 354.9370064 4260.637 0.9994801
times_uncensored_sampled[95] 96.5478941 1.586614369 101.53591227 2.3155222 26.2600870 65.8676583 129.8295324 374.2373212 4095.402 1.0000611
times_uncensored_sampled[96] 135.4466053 2.147097961 133.28368551 2.9801564 39.7669876 94.6333657 185.6312768 491.9182554 3853.455 1.0005457
times_uncensored_sampled[97] 98.4556001 1.566499538 99.20537159 3.0011606 28.0701688 69.6747813 134.7435288 367.2437428 4010.604 1.0000670
times_uncensored_sampled[98] 138.5079341 2.387405719 139.70336914 3.6575344 41.4444577 95.0014039 188.0542930 509.7029948 3424.217 1.0004408
[ reached getOption("max.print") -- omitted 678 rows ]
exp_surv_model_draws <- tidybayes::tidy_draws(exp_surv_model_fit)
exp_surv_model_draws